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Consider the Sturm-Liouville system xy+xy+y=0, 220 and y'(e)=0, y(1)=0. (a) [10 marks] Find all eigenvalues and eigenfunctions. (b) [2 marks] Are the eigenfunctions obtained

Consider the Sturm-Liouville system xy+xy+y=0, 220 and y'(e)=0, y(1)=0. (a) [10 marks] Find all eigenvalues and eigenfunctions. (b) [2 marks] Are the eigenfunctions obtained in part(a) orthogonal? Justify your answer

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